Zhang et al. [1]} have been the first ones to propose a multi-column-based architecture (Multi-Column Neural Network - MCNN) for images having arbitrary crowd density and perspective. Inspired by the success of the multi-column networks for image recognition [2]}, the proposed method claims to ensure robustness to the large variation of the object scales present in the different scenarios. The proposed architecture consists of three different branches (or columns) corresponding to filters with receptive fields of different sizes (large, medium, small). In the end, the features maps coming from the three branches are merged, and a final \(1\times 1\)  convolutional layer is responsible for predicting the final density map. We report the overview of the architecture in fig:overviewmcnn. Additionally, the authors introduced a new method for generating the ground truth crowd density maps. In contrast to existing methods that either use sum of Gaussian kernels with a fixed variance or perspective maps, they proposed to take into account the perspective distortion by estimating the spread parameters of the Gaussian kernels based on the size of the head of each person within the image. However, since it is impractical to estimate head sizes and their underlying relationship with density maps, they exploited an important property observed in high-density crowd images: the head size is related to the distance between the centers of two neighboring persons. In other words, the spread parameter for each person is data-adaptively determined based on its average distance to its neighbors. Note that the ground truth density maps created using this technique incorporate distortion information without using perspective maps. Finally, the authors introduced a new challenging dataset for the crowd counting task, the ShanghaiTech dataset, described in sec:back:datasets.
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